European Patent Nos. EP 2 184 652, EP 2 196 867 and EP 2 105 807 explain how to fabricate balance springs with curve elevation made of micro-machinable materials respectively using three parts, two parts or a single part. These documents are incorporated herein by reference.
It is known to apply the Phillips criteria to determine the theoretical curvature of a terminal curve. However, the Phillips criteria are actually an approximation which is not necessarily satisfactory if an even lower variation in rate is required.